This report introduces a new perspective on the basic concept of dependent failures where the definition of dependency is based on clustering in failure times of similar components. This perspective has two significant implications: first, it relaxes the conventional assumption that dependent failures must be simultaneous and result from a severe shock; second, it allows the analyst to use all the failures in a time continuum to estimate the potential for multiple failures in a window of time (e.g., a test interval), therefore arriving at a more accurate value for system unavailability. In addition, the models developed here provide a method for plant-specific analysis of dependency, reflecting the plant-specific maintenance practices that reduce or increase the contribution of dependent failures to system unavailability. The proposed methodology can be used for screening analysis of failure data to estimate the fraction of dependent failures among the failures. In addition, the proposed method can evaluate the impact of the observed dependency on system unavailability and plant risk. The formulations derived in this report have undergone various levels of validations through computer simulation studies and pilot applications. The pilot applications of these methodologies showed that the contribution of dependent failures of diesel generators in one plant was negligible, while in another plant was quite significant. It also showed that in the plant with significant contribution of dependency to Emergency Power System (EPS) unavailability, the contribution changed with time. Similar findings were reported for the Containment Fan Cooler breakers. Drawing such conclusions about system performance would not have been possible with any other reported dependency methodologies.